Question

The circumference of a circle is 22π
inches. Find the area of that circle. Substitute 3.14 for pi. Express your answer to the hundredths place.(1 point)
in.2

Answer 1

To find the area of the circle given its circumference, we can use the following formulas:

1. The circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]

where \( r \) is the radius of the circle.

2. The area \( A \) of a circle is given by:
\[
A = \pi r^2
\]

Given that the circumference \( C = 22\pi \) inches, we can set this equal to the formula for circumference:
\[
2\pi r = 22\pi
\]

Now, we can divide both sides by \( \pi \):
\[
2r = 22
\]

Next, divide both sides by 2 to solve for \( r \):
\[
r = 11 \text{ inches}
\]

Now that we have the radius, we can substitute it into the area formula:
\[
A = \pi r^2 = \pi (11)^2 = \pi \cdot 121
\]

Substituting \( \pi \) with 3.14:
\[
A = 3.14 \cdot 121
\]

Now, perform the multiplication:
\[
A = 3.14 \cdot 121 = 379.94
\]

Thus, the area of the circle is:
\[
\boxed{379.94} \text{ in}^2
\]